Some Global Navigation Satellite Systems (GNSS) applications require an assessment of a position solution utilizing a reduced set of available measurements. Examples of such applications are Advanced Receiver Autonomous Integrity Monitoring (ARAIM) and geometry screening. Integrity of a computed position solution refers to the measure of trust that can be placed in the correctness of information being output from the receiver. Integrity monitoring protects users from position errors arising mainly from weak geometries or satellite faults not yet identified by the system ground monitoring network.
One of the outputs of an ARAIM algorithm is a protection level bounding the integrity. Receivers using the solution separation version of the RAIM algorithm assess a number of possible subsolutions. Each subsolution is determined as a position solution based on a reduced set of satellites. To compute the protection level, the algorithm computes several statistical properties of each subsolution, including the subsolution covariance matrix, which typically requires a matrix inversion operation. Similarly high computational complexity is required to obtain the separation covariance matrix used to determine the thresholds utilized in the fault detection.
Geometry screening is an algorithm selecting the optimal subset of satellites to be used in the position solution. This will become a necessity when several GNSS constellations are operational and there is a large number of satellites in view. Using only a subset of visible satellites can reduce significantly the computational burden and if the subset is chosen properly little or no degradation in accuracy and integrity should be observed. One of the most promising ways of selecting the satellites subset is based on the subsolution covariance matrices.